I would imagine most people keep a mail address in their native country, at least a mail box rented at a US Post Office to be monitored by someone they trust, and have any bills or other statements drafted or otherwise handled electronically. Most banks prefer electronic banking statements, interaction, but I am leery of online banking, especially using Windows based computers.
More USA insurance companies are accepting and covering overseas medical care, realizing how cheap it is to do so. People get knee and hip replacements, to name but two procedures, covered by USA insurance more often these days.
Not sure how you sign of on your annual taxes, I thought you had to, but that to is done at home and by tax preparers electronically.
If you keep a car, registration is usually an annual thing.
Insurances on homes, vehicles, even on your self may need your signature or some sort of attention.
Some people give others they absolutely trust 'power of attorney' but I know one guy who did so using his daughter and she cleaned him out financially, so be careful there..